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SECTION 29.1 • Magnetic Fields and Forces 897 • When the particle’s velocity vector makes any angle ! ! 0 with the magnetic field, the magnetic force acts in a direction perpendicular to both v and B; that is, F B is perpendicular to the plane formed by v and B (Fig. 29.3a). • The magnetic force exerted on a positive charge is in the direction opposite the direction of the magnetic force exerted on a negative charge moving in the same • The magnitude of the magnetic force exerted on the moving particle is propor- tional to sin !, where ! is the angle the particle’s velocity vector makes with the B. We can summarize these observations by writing the magnetic force in the form (29.1) F B " q
v ! B (a) (b) (c) Figure 29.2 (a) Magnetic field pattern surrounding a bar magnet as displayed with iron filings. (b) Magnetic field pattern between opposite poles (N–S) of two bar magnets. (c) Magnetic field pattern between like poles (N–N) of two bar magnets. (a) F B B + q v θ (b) F B B – v v F B + Figure 29.3 The direction of the magnetic force F B acting on a charged particle moving with a velocity v in the presence of a magnetic field B. (a) The magnetic force is perpendicular to both v and B. (b) Oppositely directed magnetic forces F B are exerted on two oppositely charged particles moving at the same velocity in a magnetic field. The dashed lines show the paths of the particles, which we will investigate in Section 29.4. Henry Leap and Jim Lehman Vector expression for the magnetic force on a charged particle moving in a magnetic field |